Why is the CMB (nearly) scale invariant?

Question

Why is the power spectrum of the cosmic microwave background nearly scale-invariant? What are the mechanisms that make it deviate from the scale-invariance. And in fact: why is it scale invariant in the first place?

Does the motivation come from experiment, which is then tried to be achieved in a specific model, or directly from the model?

This post imported from StackExchange Physics at 2014-06-21 21:38 (UCT), posted by SE-user Anne O'Nyme

Comments

What makes you think it is scale invariant? The power in fluctuations on different scales varies by a factors of a few. Are you asking why it is nearly isotropic (variations on only one part in $\sim10^5$ in different directions on the sky)?

This post imported from StackExchange Physics at 2014-06-21 21:38 (UCT), posted by SE-user Kyle

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@Kyle Then my question is as follows: were the fluctuations scale invariant from the beginning (by this I mean before decoupling) and is the damping and enhancement features of the power spectrum due to Silk damping and baryonic loading which came later. Or were some fluctuation fluctuations already `preferred' wrt to others before decoupling?

This post imported from StackExchange Physics at 2014-06-21 21:38 (UCT), posted by SE-user Anne O'Nyme

Answer 1

These are just some rather handwaving comments related to why the spectrum of the fluctuations in the CMB are of expected to be scale invariant.

The variations of the CMB we observe today correspond to the expanded initial over-dense and under-dense regions created by vacuum fluctuations.

The theoretical expectation of scale invariance of the spectrum of these fluxtuations can for example be explained by looking at a scalar field with the Lagrangian density

\(L = \frac{1}{2}\dot{\phi^2} + \frac{1}{2} (\nabla\phi)^2 - V(\phi)\)

Multiplying by the volume of space $a^3(t)$, assuming that any spatial gradients are stretched out by inflation, and making use of the Euler-Lagrange equations it can be shown that the equation of motion corresponds to damped harmonic oscillator

\(\ddot{\phi} + 3 H \dot{\phi } = -\frac{\partial V}{\partial \phi}\)

where the second term in the L.H.S. is the so-called Hubble friction. Together with the quantum fluctuations, a scale invariant CMB spectrum can then theoretically be expected, as quantum fluctuations are excited at small scales, subsequently enlarged by the expansion of the universe, and finally dissipated (frozen out) by the Hubble friction at large scales as soon as their wave length gets larger than the light horizon (separation over which information can be exchanged). 

I am not sure what processes there could be that lead to deviations of the CMB spectrum from scale invariance.